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020 _a9783031617348
_9978-3-031-61734-8
024 7 _a10.1007/978-3-031-61734-8
_2doi
050 4 _aQC19.2-20.85
072 7 _aPHU
_2bicssc
072 7 _aSCI040000
_2bisacsh
072 7 _aPHU
_2thema
100 1 _aBarbu, Viorel.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_978863
245 1 0 _aNonlinear Fokker-Planck Flows and their Probabilistic Counterparts
_h[electronic resource] /
_cby Viorel Barbu, Michael Röckner.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Springer,
_c2024.
300 _aIX, 214 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x1617-9692 ;
_v2353
505 0 _a- Introduction -- Existence of nonlinear Fokker–Planck flows -- Time dependent Fokker–Planck equations -- Convergence to equilibrium of nonlinear Fokker–Planck flows -- Markov processes associated with nonlinear Fokker–Planck equations -- Appendix.
520 _aThis book delves into a rigorous mathematical exploration of the well-posedness and long-time behavior of weak solutions to nonlinear Fokker-Planck equations, along with their implications in the theory of probabilistically weak solutions to McKean-Vlasov stochastic differential equations and the corresponding nonlinear Markov processes. These are widely acknowledged as essential tools for describing the dynamics of complex systems in disordered media, as well as mean-field models. The resulting stochastic processes elucidate the microscopic dynamics underlying the nonlinear Fokker-Planck equations, whereas the solutions of the latter describe the evolving macroscopic probability distributions. The intended audience for this book primarily comprises specialists in mathematical physics, probability theory and PDEs. It can also be utilized as a one-semester graduate course for mathematicians. Prerequisites for the readers include a solid foundation in functional analysis and probability theory.
650 0 _aMathematical physics.
650 0 _aDifferential equations.
650 0 _aStochastic analysis.
_959375
650 1 4 _aMathematical Physics.
650 2 4 _aDifferential Equations.
650 2 4 _aStochastic Analysis.
_959375
700 1 _aRöckner, Michael.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_978864
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031617331
776 0 8 _iPrinted edition:
_z9783031617355
830 0 _aLecture Notes in Mathematics,
_x1617-9692 ;
_v2353
_975434
856 4 0 _uhttps://doi.org/10.1007/978-3-031-61734-8
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
912 _aZDB-2-LNM
999 _c60807
_d60807